catacaustic

Given a plane curveγ, its catacaustic (Greek ϰ⁢α⁢τ⁢α´⁢ϰ⁢α⁢υ⁢σ⁢τ⁢ι⁢ϰ⁢o´⁢ς ‘burning along’) is the envelope of a family of rays reflected from γ after having emanated from a point (which may be infinitely far, in which case the rays are initially parallel).

For example, the catacaustic of a logarithmic spiral reflecting the rays emanating from the origin is a congruent spiral. The catacaustic of the exponential curve (http://planetmath.org/ExponentialFunction) y=ex reflecting the vertical rays x=t is the catenaryy=cosh⁡(x+1).